1/2y+8/9y=5/7

Solution for 1/2y+8/9y=5/7 equation:

1/2y+8/9y=5/7

We move all terms to the left:

1/2y+8/9y-(5/7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y+8/9y-(+5/7)=0

We get rid of parentheses

1/2y+8/9y-5/7=0

We calculate fractions


(-810y^2)/882y^2+441y/882y^2+784y/882y^2=0

We multiply all the terms by the denominator


(-810y^2)+441y+784y=0

We add all the numbers together, and all the variables

(-810y^2)+1225y=0

We get rid of parentheses

-810y^2+1225y=0

a = -810; b = 1225; c = 0;
Δ = b2-4ac
Δ = 12252-4·(-810)·0
Δ = 1500625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1500625}=1225$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1225)-1225}{2*-810}=\frac{-2450}{-1620}
=1+83/162
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1225)+1225}{2*-810}=\frac{0}{-1620}
=0
$